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library(bayestestR)
df <- read_xlsx("hair_cort_dog_all.xlsx", col_types = c("text", "text",
"text", "text", "text", "text",
"text", "numeric","text", "skip",
"numeric", "skip", "skip",
"numeric", "skip"))
df <- as.data.frame(df)
dim(df) # will tell you how many rows and columns the dataset has
## [1] 73 11
class(df) # will tell you what data structure has the dataset been assigned
## [1] "data.frame"
head(df)
## number group visit season breed_group coat_colour sex age comorbidity
## 1 c1 stopped v0 winter ret dark Male 43 yes
## 2 c2 stopped v0 autumn mix dark Male 105 yes
## 3 c3 stopped v0 spring ckcs mix Female 117 yes
## 4 c4 stopped v0 summer ret dark Female 108 yes
## 5 c5 stopped v0 summer ret dark Female 110 yes
## 6 c6 stopped v0 winter mix light Female 120 yes
## fat_percent cortisol
## 1 52.21393 4.924220
## 2 38.52059 7.304202
## 3 46.94916 1.590000
## 4 44.46813 0.861570
## 5 39.59363 6.217317
## 6 NA 4.426785
numeric_df <- Filter(is.numeric, df)
describe(numeric_df) # the describe function in psych provides summary stats
## # A tibble: 3 × 26
## described_variables n na mean sd se_mean IQR skewness kurtosis
## <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 age 73 0 95.8 35.6 4.16 44 -0.104 -0.00589
## 2 fat_percent 55 18 40.5 7.82 1.05 7.82 -0.294 1.12
## 3 cortisol 73 0 8.11 16.5 1.93 5.43 4.05 18.7
## # ℹ 17 more variables: p00 <dbl>, p01 <dbl>, p05 <dbl>, p10 <dbl>, p20 <dbl>,
## # p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>,
## # p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>
plot_normality(numeric_df)
apply(numeric_df, 2, shapiro.test)
## $age
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.97361, p-value = 0.1288
##
##
## $fat_percent
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.97956, p-value = 0.4692
##
##
## $cortisol
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.46269, p-value = 6.756e-15
qqnorm(df$cortisol)
qqline(df$cortisol, col = "red")
qqnorm(log(df$cortisol))
qqline(log(df$cortisol), col = "red")
shapiro.test(log(df$cortisol))
##
## Shapiro-Wilk normality test
##
## data: log(df$cortisol)
## W = 0.94725, p-value = 0.004126
summary(df$cortisol)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4141 1.4119 2.3331 8.1089 6.8455 104.6172
summary(log(df$cortisol))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.8817 0.3449 0.8472 1.1816 1.9236 4.6503
df$lgCort <- log(df$cortisol)
summary(df$lgCort)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.8817 0.3449 0.8472 1.1816 1.9236 4.6503
hist(df$lgCort)
df$breed <- df$breed_group
df$breed <- factor(df$breed, levels = c("mix", "ckcs", "pug", "ret", "other"))
head(df$breed)
## [1] ret mix ckcs ret ret mix
## Levels: mix ckcs pug ret other
df$coat_colour <- factor(df$coat_colour, levels = c("light", "mix", "dark"), ordered = FALSE)
head(df$coat_colour)
## [1] dark dark mix dark dark light
## Levels: light mix dark
sumtable(df)
| Variable | N | Mean | Std. Dev. | Min | Pctl. 25 | Pctl. 75 | Max |
|---|---|---|---|---|---|---|---|
| group | 73 | ||||||
| … completed | 42 | 58% | |||||
| … stopped | 31 | 42% | |||||
| visit | 73 | ||||||
| … v0 | 52 | 71% | |||||
| … v1 | 21 | 29% | |||||
| season | 73 | ||||||
| … autumn | 21 | 29% | |||||
| … spring | 14 | 19% | |||||
| … summer | 22 | 30% | |||||
| … winter | 16 | 22% | |||||
| breed_group | 73 | ||||||
| … ckcs | 7 | 10% | |||||
| … mix | 16 | 22% | |||||
| … other | 26 | 36% | |||||
| … pug | 7 | 10% | |||||
| … ret | 17 | 23% | |||||
| coat_colour | 73 | ||||||
| … light | 27 | 37% | |||||
| … mix | 16 | 22% | |||||
| … dark | 30 | 41% | |||||
| sex | 73 | ||||||
| … Female | 43 | 59% | |||||
| … Male | 30 | 41% | |||||
| age | 73 | 96 | 36 | 16 | 73 | 117 | 182 |
| comorbidity | 73 | ||||||
| … no | 15 | 21% | |||||
| … yes | 58 | 79% | |||||
| fat_percent | 55 | 40 | 7.8 | 18 | 37 | 45 | 61 |
| cortisol | 73 | 8.1 | 16 | 0.41 | 1.4 | 6.8 | 105 |
| lgCort | 73 | 1.2 | 1.2 | -0.88 | 0.34 | 1.9 | 4.7 |
| breed | 73 | ||||||
| … mix | 16 | 22% | |||||
| … ckcs | 7 | 10% | |||||
| … pug | 7 | 10% | |||||
| … ret | 17 | 23% | |||||
| … other | 26 | 36% |
par(mfrow = c(1,1))
vioplot(lgCort ~ breed, col = "firebrick",
data = df)
stripchart(lgCort ~ breed, vertical = TRUE, method = "jitter",
col = "steelblue3", data = df, pch = 20)
par(mfrow = c(1,1))
vioplot(lgCort ~ coat_colour, col = "firebrick",
data = df)
stripchart(lgCort ~ coat_colour, vertical = TRUE, method = "jitter",
col = "steelblue3", data = df, pch = 20)
df$slgCort <- standardize(df$lgC)
summary(df$slgCort)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.7079 -0.6925 -0.2768 0.0000 0.6142 2.8713
hist(df$slgCort)
df2 <- na.omit(df)
model <- brm(slgCort ~ coat_colour + breed + + (1 | visit), family = skew_normal(), data = df)
Rationale… casual diagram implies that breed is a counfounder for the effect of hair colour on hair cortsol. Therefore, need to include in the model.
default_prior(slgCort ~ coat_colour + breed + + (1 | visit),
family = skew_normal(),
data = df)
## prior class coef group resp dpar nlpar lb ub
## normal(0, 4) alpha
## (flat) b
## (flat) b breedckcs
## (flat) b breedother
## (flat) b breedpug
## (flat) b breedret
## (flat) b coat_colourdark
## (flat) b coat_colourmix
## student_t(3, -0.3, 2.5) Intercept
## student_t(3, 0, 2.5) sd 0
## student_t(3, 0, 2.5) sd visit 0
## student_t(3, 0, 2.5) sd Intercept visit 0
## student_t(3, 0, 2.5) sigma 0
## source
## default
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## default
## (vectorized)
## (vectorized)
## default
No published data about effects on breed, but this is plausible However, unclear as to which breeds will differ and which way. Therefore, use a regularising prior but keep it neutral and broad.
In one study, dogs with a light coat colour had greater log (hair cortisol) than those with a mix or dark colour. Effect was small e.g. 0.070 (mix) or 0.075 (dark). There can justify a prior of that magnitideu, but keep general and regularising REF: Bowland. Front. Vet. Sci. 7:565346. doi: 10.3389/fvets.2020.565346
# Set individual priors
prior_int <- set_prior("normal(0, 0.5)", class = "Intercept")
prior_sig <- set_prior("exponential(1)", class = "sigma")
prior_b <- set_prior("normal(0, 1)", class = "b")
prior_b_coat_m <- set_prior("normal(-0.070, 1)", class = "b", coef = "coat_colourmix")
prior_b_coat_d <- set_prior("normal(-0.075, 1)", class = "b", coef = "coat_colourdark")
prior_sd <- set_prior("normal(0, 1)", class = "sd")
prior_alpha <- set_prior("normal(4, 2)", class = "alpha")
# Combine priors into list
priors <- c(prior_int, prior_sig, prior_b, prior_b_coat_m, prior_b_coat_d, prior_sd, prior_alpha)
x <- seq(-3, 3, length.out = 100)
y <- dnorm(x, mean = 0, sd = 0.5)
plot(y ~ x, type = "l")
x <- seq(0, 3, length.out = 100)
y <- dexp(x, rate = 1)
plot(y ~ x, type = "l")
Based on distribution of log normal hair cortisol, expect things to be skewed to the right. Try different levels of alpha for skew normal… and an alpha of 4 seems to be a good fit for the shape of the skew in the log hair cortisol for this dataset
x <- seq(-3, 5, length.out = 100)
y <- dskew_normal(x, mu = 0, sigma = 1, alpha = 4)
plot(y ~ x, type = "l")
x <- seq(-3, 3, length.out = 100)
y <- dnorm(x, mean = -0.07, sd = 1)
plot(y ~ x, type = "l")
x <- seq(-3, 3, length.out = 100)
y <- dnorm(x, mean = -0.075, sd = 1)
plot(y ~ x, type = "l")
Increased adapt_delta >0.8 (0.9 here), as had divergent transitions
set.seed(666)
model <- brm(slgCort ~ coat_colour + breed + (1 | visit),
family = skew_normal(),
prior = priors,
data = df,
control=list(adapt_delta=0.999, stepsize = 0.001, max_treedepth =15),
iter = 8000, warmup = 2000,
cores = 4,
save_pars = save_pars(all =TRUE),
sample_prior = TRUE)
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.0.13.5)’
## using SDK: ‘MacOSX15.5.sdk’
## clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/opt/R/arm64/include -fPIC -falign-functions=64 -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
## /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
## 679 | #include <cmath>
## | ^~~~~~~
## 1 error generated.
## make: *** [foo.o] Error 1
## Start sampling
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
summary(model)
## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: slgCort ~ coat_colour + breed + (1 | visit)
## Data: df (Number of observations: 73)
## Draws: 4 chains, each with iter = 8000; warmup = 2000; thin = 1;
## total post-warmup draws = 24000
##
## Multilevel Hyperparameters:
## ~visit (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.38 0.36 0.01 1.35 1.00 7766 8157
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.19 0.34 -0.49 0.86 1.00 10234 12473
## coat_colourmix -0.50 0.29 -1.06 0.07 1.00 14208 15167
## coat_colourdark -0.33 0.23 -0.78 0.13 1.00 15303 16240
## breedckcs 0.22 0.37 -0.54 0.91 1.00 15883 15971
## breedpug -0.06 0.37 -0.80 0.65 1.00 14545 15719
## breedret -0.04 0.29 -0.61 0.51 1.00 14158 16886
## breedother 0.10 0.25 -0.39 0.61 1.00 14064 15235
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.02 0.09 0.85 1.22 1.00 18453 16951
## alpha 4.44 1.44 1.97 7.59 1.00 16907 13996
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
plot(model)
Looking for hairy caterpillars
mcmc_plot(model, type = 'rank_overlay')
Usually better than the compatability intervals given in the summary
draws <- as.matrix(model)
HPDI(draws[,2], 0.97)
## |0.97 0.97|
## -1.1269354 0.1290574
Usually better than the compatability intervals given in the summary
draws <- as.matrix(model)
HPDI(draws[,3], 0.97)
## |0.97 0.97|
## -0.8304157 0.1737404
bayes_R2(model, probs = c(0.015, 0.5, 0.985)) # 0.015, 0.5, 0.985 are the quantiles
## Estimate Est.Error Q1.5 Q50 Q98.5
## R2 0.08756415 0.03930199 0.02095567 0.08274138 0.1862381
loo_R2(model, probs = c(0.015, 0.5, 0.985)) # 0.015, 0.5, 0.985 are the quantiles
## Warning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
## Estimate Est.Error Q1.5 Q50 Q98.5
## R2 -0.09748751 0.05196706 -0.2278252 -0.09371635 0.001627205
checks whether actual data is similar to simulated data.
pp_check(model, ndraws = 100)
par(mfrow = c(1,1))
pp_check(model, type = "hist", ndraws = 11, binwidth = 0.25) # separate histograms of 11 MCMC draws vs actual data
pp_check(model, type = "error_hist", ndraws = 11) # separate histograms of errors for 11 draws
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
pp_check(model, type = "scatter_avg", ndraws = 100) # scatter plot
pp_check(model, type = "stat_2d") # scatterplot of joint posteriors
## Using all posterior draws for ppc type 'stat_2d' by default.
## Note: in most cases the default test statistic 'mean' is too weak to detect anything of interest.
# PPC functions for predictive checks based on (approximate) leave-one-out (LOO) cross-validation
pp_check(model, type = "loo_pit_overlay", ndraws = 1000)
## Warning: Found 2 observations with a pareto_k > 0.7 in model '.x1'. We
## recommend to set 'moment_match = TRUE' in order to perform moment matching for
## problematic observations.
## NOTE: The kernel density estimate assumes continuous observations and is not optimal for discrete observations.
pp_check(model, type = "error_scatter_avg")
## Using all posterior draws for ppc type 'error_scatter_avg' by default.
pairs(model)
loo_model <- loo(model, moment_match = TRUE)
loo_model
##
## Computed from 24000 by 73 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -104.4 6.1
## p_loo 7.8 1.6
## looic 208.7 12.1
## ------
## MCSE of elpd_loo is 0.0.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.5, 1.2]).
##
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.
First, check the sensitivity of the prior and likelihood to power-scaling. Posterior and posteriors resulting from power-scaling.
powerscale_sensitivity(model, variable = c("b_Intercept", "sigma", "b_breedckcs", "b_breedother", "b_breedpug", "b_breedret", "b_coat_colourmix", "b_coat_colourdark"))
## Sensitivity based on cjs_dist
## Prior selection: all priors
## Likelihood selection: all data
##
## variable prior likelihood diagnosis
## b_Intercept 0.036 0.047 -
## sigma 0.032 0.171 -
## b_breedckcs 0.022 0.100 -
## b_breedother 0.013 0.078 -
## b_breedpug 0.022 0.077 -
## b_breedret 0.013 0.080 -
## b_coat_colourmix 0.030 0.105 -
## b_coat_colourdark 0.023 0.103 -
powerscale_plot_dens(model, variable = c("b_Intercept", "sigma", "b_breedckcs", "b_breedother", "b_breedpug", "b_breedret", "b_coat_colourmix", "b_coat_colourdark"), facet_rows = "variable")
powerscale_plot_ecdf(model, variable = c("b_Intercept", "sigma", "b_breedckcs", "b_breedother", "b_breedpug", "b_breedret", "b_coat_colourmix", "b_coat_colourdark"), facet_rows = "variable")
powerscale_plot_quantities(model, variable = c("b_Intercept", "sigma", "b_breedckcs", "b_breedother", "b_breedpug", "b_breedret", "b_coat_colourmix", "b_coat_colourdark"), facet_rows = "variable")
check_prior(model, effects = "all")
## Parameter Prior_Quality
## 1 b_Intercept informative
## 2 b_coat_colourmix informative
## 3 b_coat_colourdark informative
## 4 b_breedckcs informative
## 5 b_breedpug informative
## 6 b_breedret informative
## 7 b_breedother informative
## 8 sd_visit__Intercept informative
These values appear similar to what was set for the priors, so seems OK?
prior <- prior_draws(model)
prior %>% glimpse()
## Rows: 24,000
## Columns: 10
## $ Intercept <dbl> 0.96084670, 0.46491481, -0.26462236, 0.69449626, 0.3…
## $ b_coat_colourmix <dbl> -0.28799106, 0.07935388, 0.18844207, 0.50087819, -0.…
## $ b_coat_colourdark <dbl> 0.94357599, -0.39174170, -0.27564698, -0.74237982, -…
## $ b_breedckcs <dbl> 0.64610478, 0.53333003, 1.64518765, 0.67336808, -0.8…
## $ b_breedpug <dbl> -1.42358243, 0.13827681, -0.95022571, -0.91958273, -…
## $ b_breedret <dbl> -0.40108365, 1.44152867, -0.52672062, 0.41224951, 0.…
## $ b_breedother <dbl> -0.51285359, 1.37645411, 0.87299377, 0.72529536, -1.…
## $ sigma <dbl> 0.51944386, 0.44354540, 0.84031239, 0.35286383, 0.16…
## $ alpha <dbl> 5.8251935, 3.5256696, 6.2386522, 3.3732770, 3.146630…
## $ sd_visit <dbl> 0.09234196, 0.33199112, 0.11917467, 1.27825643, 0.66…
set.seed(5)
prior %>%
slice_sample(n = 50) %>%
rownames_to_column("draw") %>%
expand_grid(a = c(0, 1)) %>%
mutate(c = Intercept + b_coat_colourmix * a) %>%
ggplot(aes(x = a, y = c)) +
geom_line(aes(group = draw),
color = "firebrick", alpha = .4) +
geom_point(color = "firebrick", size = 2) +
labs(x = "Breed",
y = "log(cort) (std)") +
coord_cartesian(ylim = c(-3, 3)) +
theme_bw() +
theme(panel.grid = element_blank())
set.seed(5)
prior %>%
slice_sample(n = 50) %>%
rownames_to_column("draw") %>%
expand_grid(a = c(0, 1)) %>%
mutate(c = Intercept + b_coat_colourdark * a) %>%
ggplot(aes(x = a, y = c)) +
geom_line(aes(group = draw),
color = "firebrick", alpha = .4) +
geom_point(color = "firebrick", size = 2) +
labs(x = "Breed",
y = "log(cort) (std)") +
coord_cartesian(ylim = c(-3, 3)) +
theme_bw() +
theme(panel.grid = element_blank())
Can simulate data just on the priors. Fit model but only consider prior when fitting model. If this looks reasonable, it helps to confirm that your priors were reasonable
set.seed(666)
model_priors_only <- brm(slgCort ~ coat_colour + breed + (1 | visit),
family = skew_normal(),
prior = priors,
data = df,
sample_prior = "only")
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.0.13.5)’
## using SDK: ‘MacOSX15.5.sdk’
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## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
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## /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
## 679 | #include <cmath>
## | ^~~~~~~
## 1 error generated.
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## Start sampling
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pp_check(model_priors_only, ndraws = 100)
as_draws_df(model) %>%
select(b_Intercept:sigma) %>%
cov() %>%
round(digits = 3)
## Warning: Dropping 'draws_df' class as required metadata was removed.
## b_Intercept b_coat_colourmix b_coat_colourdark b_breedckcs
## b_Intercept 0.113 -0.039 -0.026 -0.024
## b_coat_colourmix -0.039 0.082 0.031 -0.015
## b_coat_colourdark -0.026 0.031 0.053 -0.012
## b_breedckcs -0.024 -0.015 -0.012 0.135
## b_breedpug -0.053 0.036 0.021 0.023
## b_breedret -0.043 0.022 -0.002 0.030
## b_breedother -0.037 0.007 -0.005 0.032
## sd_visit__Intercept 0.002 -0.001 -0.002 -0.006
## sigma 0.004 0.000 0.000 0.000
## b_breedpug b_breedret b_breedother sd_visit__Intercept
## b_Intercept -0.053 -0.043 -0.037 0.002
## b_coat_colourmix 0.036 0.022 0.007 -0.001
## b_coat_colourdark 0.021 -0.002 -0.005 -0.002
## b_breedckcs 0.023 0.030 0.032 -0.006
## b_breedpug 0.137 0.041 0.035 -0.001
## b_breedret 0.041 0.081 0.037 -0.001
## b_breedother 0.035 0.037 0.063 0.000
## sd_visit__Intercept -0.001 -0.001 0.000 0.132
## sigma 0.000 0.000 0.000 -0.001
## sigma
## b_Intercept 0.004
## b_coat_colourmix 0.000
## b_coat_colourdark 0.000
## b_breedckcs 0.000
## b_breedpug 0.000
## b_breedret 0.000
## b_breedother 0.000
## sd_visit__Intercept -0.001
## sigma 0.009
NB Uses posterior_predict
# use posterior predict to simulate predictions
ppd <- posterior_predict(model)
par(mfrow = c(2,2))
stripchart(slgCort ~ coat_colour, vertical = TRUE, method = "jitter",
col = "steelblue3", data = df, pch = 20, main = "Observed")
stripchart(ppd[sample(seq(1, dim(ppd)[1]), 1),] ~ coat_colour, vertical = TRUE, method = "jitter",
col = "firebrick", data = df, pch = 20, main = "PPD")
stripchart(ppd[sample(seq(1, dim(ppd)[1]), 1),] ~ coat_colour, vertical = TRUE, method = "jitter",
col = "firebrick", data = df, pch = 20, main = "PPD")
stripchart(ppd[sample(seq(1, dim(ppd)[1]), 1),] ~ coat_colour, vertical = TRUE, method = "jitter",
col = "firebrick", data = df, pch = 20, main = "PPD")
plot(conditional_effects(model), ask = FALSE)
ce <- conditional_effects(model, effects = "coat_colour")
ce_df <- ce[[1]][c(1, 7:10)]
ggplot(ce_df, aes(x=coat_colour, y=estimate__, group=1)) +
geom_errorbar(width=.1, aes(ymin=lower__, ymax=upper__), colour=c("#F8766D", "#00BFC4","#7CAE00"), linewidth = 1) +
geom_point(shape=21, size=6, fill=c("#F8766D", "#00BFC4","#7CAE00")) +
theme_bw() +
labs(title = "Conditional effect of coat colour on hair cortisol") +
labs(y = paste0("Log Hair Cortisol (standardised)")) +
labs(x = paste0("Coat colour")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey25", size = 12),
axis.text.y = element_text(color = "grey50", size = 10))
mcmc_plot(model,
variable = c("b_coat_colourmix",
"b_coat_colourdark",
"b_breedckcs",
"b_breedother",
"b_breedpug",
"b_breedret"))
mcmc_plot(model,
variable = c("b_coat_colourmix", "prior_b_coat_colourmix",
"b_coat_colourdark", "prior_b_coat_colourdark"))
mcmc_plot(model,
variable = c("b_coat_colourmix", "prior_b_coat_colourmix",
"b_coat_colourdark", "prior_b_coat_colourdark"),
type = "areas") +
theme_classic() +
labs(title = "Prior vs posterior distribution for coat colour effect") +
labs(y = "") +
labs(x = paste0("Possible parameter values")) +
scale_y_discrete(labels=c("prior_b_coat_colourmix" = "Prior for mixed", "b_coat_colourmix" = "Posterior for mixed",
"prior_b_coat_colourdark" = "Prior for dark", "b_coat_colourdark" = "Posterior for dark"),
limits = c("prior_b_coat_colourmix", "b_coat_colourmix",
"prior_b_coat_colourdark", "b_coat_colourdark")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey50", size = 12),
axis.text.y = element_text(color = "grey8",size = 12))
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
mcmc_plot(model,
variable = c("b_Intercept", "sigma",
"b_coat_colourmix",
"b_coat_colourdark",
"b_breedckcs",
"b_breedother",
"b_breedpug",
"b_breedret"))
posterior <- as.matrix(model)
mcmc_areas(posterior,
pars = c("Intercept", "sigma",
"b_coat_colourmix",
"b_coat_colourdark",
"b_breedckcs",
"b_breedother",
"b_breedpug",
"b_breedret"),
# arbitrary threshold for shading probability mass
prob = 0.75)
posterior <- as.matrix(model)
mcmc_areas(posterior,
pars = c("b_coat_colourmix",
"b_coat_colourdark",
"b_breedckcs",
"b_breedother",
"b_breedpug",
"b_breedret"),
prob = 0.75) # arbitrary threshold for shading probability mass
posterior <- as.matrix(model)
mcmc_areas(posterior,
pars = c("b_coat_colourmix",
"b_coat_colourdark"),
# arbitrary threshold for shading probability mass
prob = 0.97) +
theme_classic() +
labs(title = "Posterior distribution for coat colour effect",
y = "Density distribution",
x = "Possible parameter values") +
scale_y_discrete(labels=c("b_coat_colourmix" = "Mixed",
"b_coat_colourdark" = "Dark")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey50", size = 12),
axis.text.y = element_text(color = "grey8",size = 12))
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
# Focus on describing posterior
hdi_range <- hdi(model, ci = c(0.65, 0.70, 0.80, 0.89, 0.95))
plot(hdi_range, show_intercept = T)
# Focus on describing posterior
hdi_range <- hdi(model, ci = c(0.65, 0.70, 0.80, 0.89, 0.95),
parameters = c("b_coat_colourmix",
"b_coat_colourdark"))
plot(hdi_range, show_intercept = T) +
labs(title = "Posterior distribution for coat colour effect") +
labs(y = "Density distribution") +
labs(x = "Possible parameter values") +
scale_y_discrete(labels=c("b_coat_colourmix" = "Mixed",
"b_coat_colourdark" = "Dark"),
limits = c("b_coat_colourmix", "b_coat_colourdark")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey50", size = 12),
axis.text.y = element_text(color = "grey8",size = 12))
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
draws <- as.matrix(model)
mean(draws[,2] <0)
## [1] 0.9577917
mean(draws[,2] >0)
## [1] 0.04220833
HPDI(draws[,2], prob=0.97)
## |0.97 0.97|
## -1.1269354 0.1290574
draws <- as.matrix(model)
mean(draws[,3] <0)
## [1] 0.9282917
mean(draws[,3] >0)
## [1] 0.07170833
HPDI(draws[,3], prob=0.97)
## |0.97 0.97|
## -0.8304157 0.1737404
# create new dataframe which contains results of the first dog
new_data <- rbind(df[1,], df[1,], df[1,])
# Now change one category to be different
new_data$coat_colour <- c("light", "dark", "mix")
# Visualise df to make sure it has worked
new_data
## number group visit season breed_group coat_colour sex age comorbidity
## 1 c1 stopped v0 winter ret light Male 43 yes
## 2 c1 stopped v0 winter ret dark Male 43 yes
## 3 c1 stopped v0 winter ret mix Male 43 yes
## fat_percent cortisol lgCort breed slgCort
## 1 52.21393 4.92422 1.594166 ret 0.3415375
## 2 52.21393 4.92422 1.594166 ret 0.3415375
## 3 52.21393 4.92422 1.594166 ret 0.3415375
# Now get mean predictions from the draws of the model
pred_means <- posterior_predict(model, newdata = new_data)
# Compare difference in means for coat colours vs light
differenceLM <- pred_means[,1] - pred_means[,2]
differenceDM <- pred_means[,1] - pred_means[,3]
par(mfrow = c(2,2))
# Examine mean of difference
mean(differenceLM)
## [1] 0.3495764
# View histogram of this
hist(differenceLM)
# Create HPDI
HPDI(differenceLM, 0.93)
## |0.93 0.93|
## -2.376492 2.991906
# Examine mean of difference
mean(differenceDM)
## [1] 0.5096972
# View histogram of this
hist(differenceDM)
# Create HPDI
HPDI(differenceDM, 0.93)
## |0.93 0.93|
## -2.267171 3.163406
# create new dataframe which contains results of all dogs
new_data1 <- df
# Now change one category to be different
new_data1$coat_colour <- c("light")
# create new dataframe which contains results of the all dopgs
new_data2 <- df
# Now change one category to be different
new_data1$coat_colour <- c("mix")
# Now get predictions from the draws of the models
pred_nd1 <- posterior_predict(model, newdata = new_data1)
pred_nd2 <- posterior_predict(model, newdata = new_data2)
pred_diff <- pred_nd1 - pred_nd2
pred_diff <- data.frame(pred_diff)
# Create mean of differences for each column (dog) of the dataframe
pred_diff_LM <- apply(pred_diff, 2, mean)
# View histogram of mean differences
hist(pred_diff_LM)
# Examine mean of difference
mean(pred_diff_LM)
## [1] -0.2536659
# View histogram of this
HPDI(pred_diff_LM, 0.97)
## |0.97 0.97|
## -0.51743424 0.01037813
# create new dataframe which contains results of the first dog
new_data2 <- df
# Now change one category to be different
new_data2$coat_colour <- c("dark")
# Now get predictions from the draws of the models
pred_nd1 <- posterior_predict(model, newdata = new_data1)
pred_nd2 <- posterior_predict(model, newdata = new_data2)
pred_diff <- pred_nd1 - pred_nd2
pred_diff <- data.frame(pred_diff)
# Create mean of differences for each column (dog) of the dataframe
pred_diff_DM <- apply(pred_diff, 2, mean)
# View histogram of mean differences
hist(pred_diff_DM)
# Examine mean of difference
mean(pred_diff_DM)
## [1] -0.1641008
# View histogram of this
HPDI(pred_diff_DM, 0.97)
## |0.97 0.97|
## -0.1771495 -0.1446354
set.seed(666)
nd <- tibble(visit = 'v0', coat_colour = c("light", "dark", "mix"), breed = "mix")
p1 <-
predict(model,
resp = "slgCort",
newdata = nd) %>%
data.frame() %>%
bind_cols(nd) %>%
ggplot(aes(x = coat_colour, y = Estimate, ymin = Q2.5, ymax = Q97.5)) +
geom_linerange(aes(ymin = Q2.5, ymax = Q97.5),
linewidth = 1, color = "#F8766D", alpha = 3/5) +
geom_point(size = 5, color = "#F8766D") +
theme_bw() +
labs(title = "Predicted effect of coat colour on hair cortisol") +
labs(y = paste0("Log hair cortisol (standardised)")) +
labs(x = paste0("Coat colour")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5)) +
coord_cartesian(ylim = c(-2.5, 2.5))
plot(p1)
pred_slgCort <- posterior_epred(model)
av_pred_slgCort <- colMeans(pred_slgCort)
plot(av_pred_slgCort ~ df$slgCort)
# Set individual priors
prior_int <- set_prior("normal(0, 1.0)", class = "Intercept")
prior_b <- set_prior("normal(0, 1)", class = "b")
prior_b_coat_m <- set_prior("normal(-0.070, 1)", class = "b", coef = "coat_colourmix")
prior_b_coat_d <- set_prior("normal(-0.075, 1)", class = "b", coef = "coat_colourdark")
prior_sd <- set_prior("normal(0, 1)", class = "sd")
prior_alpha <- set_prior("normal(4, 2)", class = "alpha")
# Combine priors into list
priors2 <- c(prior_int, prior_b, prior_b_coat_m, prior_b_coat_d, prior_sd, prior_alpha)
Increased adapt_delta >0.8 (0.9 here), as had divergent transitions
set.seed(666)
model2 <- brm(bf(slgCort ~ coat_colour + breed + (1 | visit),
sigma ~ coat_colour),
family = skew_normal(),
prior = priors2,
data = df,
control=list(adapt_delta=0.999, stepsize = 0.001, max_treedepth =15),
iter = 8000, warmup = 2000,
cores = 4,
save_pars = save_pars(all =TRUE),
sample_prior = TRUE)
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.0.13.5)’
## using SDK: ‘MacOSX15.5.sdk’
## clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/opt/R/arm64/include -fPIC -falign-functions=64 -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
## /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
## 679 | #include <cmath>
## | ^~~~~~~
## 1 error generated.
## make: *** [foo.o] Error 1
## Start sampling
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
summary(model2)
## Family: skew_normal
## Links: mu = identity; sigma = log; alpha = identity
## Formula: slgCort ~ coat_colour + breed + (1 | visit)
## sigma ~ coat_colour
## Data: df (Number of observations: 73)
## Draws: 4 chains, each with iter = 8000; warmup = 2000; thin = 1;
## total post-warmup draws = 24000
##
## Multilevel Hyperparameters:
## ~visit (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.41 0.40 0.01 1.52 1.00 8056 10037
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 0.20 0.42 -0.66 1.04 1.00 9308
## sigma_Intercept 0.01 0.15 -0.27 0.32 1.00 15896
## coat_colourmix -0.36 0.36 -1.03 0.39 1.00 15556
## coat_colourdark -0.37 0.26 -0.88 0.14 1.00 15683
## breedckcs 0.19 0.37 -0.58 0.89 1.00 17541
## breedpug -0.06 0.37 -0.79 0.68 1.00 16540
## breedret -0.06 0.28 -0.60 0.48 1.00 14423
## breedother 0.08 0.26 -0.41 0.59 1.00 15227
## sigma_coat_colourmix 0.16 0.24 -0.30 0.64 1.00 15193
## sigma_coat_colourdark -0.06 0.21 -0.47 0.35 1.00 14666
## Tail_ESS
## Intercept 10287
## sigma_Intercept 14670
## coat_colourmix 15787
## coat_colourdark 16443
## breedckcs 16697
## breedpug 15206
## breedret 15219
## breedother 13731
## sigma_coat_colourmix 16148
## sigma_coat_colourdark 16093
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## alpha 4.48 1.45 2.02 7.66 1.00 19208 14884
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
loo_model2 <- loo(model2, moment_match = TRUE)
loo_model2
##
## Computed from 24000 by 73 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -106.4 6.3
## p_loo 9.8 1.8
## looic 212.8 12.6
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.6, 1.2]).
##
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.
model <- add_criterion(model, "loo")
## Warning: Found 2 observations with a pareto_k > 0.7 in model 'model'. We
## recommend to set 'moment_match = TRUE' in order to perform moment matching for
## problematic observations.
model2 <- add_criterion(model2, "loo")
## Warning: Found 1 observations with a pareto_k > 0.7 in model 'model2'. We
## recommend to set 'moment_match = TRUE' in order to perform moment matching for
## problematic observations.
loo_compare(model, model2)
## elpd_diff se_diff
## model 0.0 0.0
## model2 -2.1 0.9
Model 1 is a better fit so keep this